A time interpolator circuit increases the resolution and accuracy of time measurements beyond the limits of digital circuits. Time interpolators are commonly used in frequency counters, which are instruments that measure the number of cycles of a repetitive signal per second. In a typical reciprocal frequency counter, a digital circuit counts the number of electronic clock pulses that occur per cycle of a signal to be measured. The frequency is then proportional to the reciprocal of this number. In actual practice most frequency counters count the number of clock pulses that occur during a large number of signal cycles. Thus the counter may start counting clock pulses at one cycle of the signal and stop millions of signal cycles later.
As an example, suppose that a frequency counter has a clock that runs at 10 MHz and the signal to be measured has a frequency of roughly 1 GHz. The counter begins counting clock pulses at one signal cycle and stops 100 million signal cycles later. Suppose that 999,437 clock pulses are counted between the first and 100 millionth signal cycles. This result means that the frequency of the nominally 1 GHz signal is actually about 1.000563 GHz (100 million signal cycles divided by 0.0999437 seconds). It may not be exactly 1.000563 GHz, however, because the time between the first signal cycle and the first clock pulse, and the time between the last signal cycle and the last clock pulse, haven't been measured. A time interpolator is a circuit that accounts for these fractional times to improve measurement accuracy.
An early time interpolator circuit example is described in “Electronic interpolating counter for the time interval and frequency measurement” by Bagley and Brooksby (U.S. Pat. No. 3,133,189), and numerous variations and improvements have followed. Many interpolators rely on the charging characteristics of a capacitor connected to a current source. The voltage across such a capacitor is:
  V  =            1      C        ⁢          ∫              I        ⁢                  ⅆ          t                    where V is the voltage, C is the capacitance and I is the current flowing into the capacitor. If I is constant, as is the case with a good quality current source, then:
  V  =            (              I        C            )        ⁢    t  Thus, the voltage across the capacitor is directly proportional to the time during which current is allowed to flow into it. Furthermore, this voltage can be measured quite accurately and precisely with an analog-to-digital converter.
Despite the long history of interpolator circuits, room for improvements exists. Thus what is needed is a simple, accurate interpolator circuit appropriate for modern frequency counters and similar devices.